The activity has raised the possibility of improved relations between the two countries, whose ties have been marked by mutual antipathy and mistrust since the 1979 Islamic revolution.

But as Parallels' Greg Myre noted upon Rouhani's election in June, we've heard this story before — several times. Greg wrote:

"Ever since Iran's 1979 Islamic Revolution, the U.S. has been in search of moderate Iranian leaders who could steer the country away from its hostile standoff with America.

"To cite one famous example, President Ronald Reagan's administration secretly sold weapons to Iran in the mid-1980s in the belief it could work with the country's 'moderate' elements even as Iran remained under the control of revolutionary leader Ayatollah Ruhollah Khomeini."

There were also bouts of optimism during the presidencies of Akbar Hashemi Rafsanjani and Mohammed Khatami — but in the end, the stalemate remained.

What's Different This Time?

Well, for one, Rouhani, a cleric who's held prominent positions since the 1979 revolution, including a stint as a nuclear negotiator, appears to have the backing of Iran's Supreme Leader Ayatollah Ali Khamenei, who under Iran's political system outranks the president and has final say.

"We've had overtures in the past, those were more or less sincere," says Suzanne Maloney, a senior fellow at the Brookings Institution. "The distinction is that it's the first time in Iran's modern political history that there's been a consensus among relevant decision-makers to deal with Washington and overcome the difficulties that Iran faces."

The apparent buy-in from the supreme leader is significant, says Karim Sadjadpour, a senior associate at the Carnegie Endowment for International Peace.

"The supreme leader himself has advocated a term that's very rare for him: He called for 'heroic flexibility' in Iran's diplomacy," Sadjadpour told Morning Edition. "And this is someone who over the course of his three decades' tenure as supreme leader has really displayed heroic inflexibility."

Why Now?

"It's all about sanctions relaxation at this stage," says Maloney, who previously worked at the State Department's policy planning office. "They've cut the Iranian banking system off from the international banking system."

Iran's economy has been crippled by the sanctions. Oil exports have fallen sharply, inflation is high, its currency has crashed and unemployment is up.

But, as Sadjadpour notes, it's unclear if the diplomatic overtures from Iran are "just tactical flexibility in order to stave off economic pressure and reduce sanctions or ... [whether] Iran really [is] thinking about changing ... [its] longstanding strategic principles."

"The other piece is that Iran is most urgently focused on the nuclear issue, but there are a lot of other moving parts: Syria, the nascent revival of the Arab-Israeli peace process," she says. "Iran is a heavily invested adversary of American aims in both of those arenas."

Israel's View

Israel views all of this warily. It sees Iran's nuclear program as an existential threat (though Iran maintains that the program is for peaceful purposes only), and says the Iranian regime has a history of lying and that it cannot be trusted.

"There's a lot of spin coming out of Iran right now," Michael Oren, Israel's outgoing ambassador to the U.S., told All Things Considered. "They're denying that they're denying the Holocaust, and saying they want to negotiate but not meeting the demands of the Security Council to stop enrichment, to ship their stockpiles abroad.

"That's spin, but the centrifuges continue to spin in Tehran, enriching uranium."

Sadjadpour notes the mistrust between Iran and the U.S. is so deep "it's not going to be erased overnight with a few conciliatory tweets from Hassan Rouhani or a statement from the supreme leader."

He says that for there to be progress between the two countries, Rouhani would have to cap Iran's uranium enrichment at a certain level, allow more U.N. inspections of the country's nuclear sites and be more transparent about the nuclear program.

But there are other issues, too: Iran's support for Hezbollah, its rejection of Israel's existence, its support for the Assad regime in Syria — all of which are going to be "much more difficult for Rouhani to change."

"I would argue that, in fact, it's those issues which have been the perennial source of tension between Washington and Tehran – particularly the U.S. Congress," he said. "As someone once told me: In the context of domestic U.S. politics, a country can enrich uranium and it can call for Israel's demise, but it can't do both at the same time."